Inharmonicity

In music, inharmonicity is the degree to which the frequencies of overtones (also known as partials or partial tones) depart from whole multiples of the fundamental frequency (harmonic series). Acoustically, a note perceived to have a single distinct pitch actually contains a variety of additional overtones. Many percussion instruments, such as cymbals, tam-tams, and chimes, create complex and inharmonic sounds.

Music harmony and intonation depends strongly on the harmonicity of tones. In any real musical instrument, the resonant body that produces the music tone—typically a string, wire, or column of air—deviates from the ideal and has some amount of inharmonicity. For example, a very thick string behaves less like an ideal string and more like a cylinder, which has natural resonances that are not whole number multiples of the fundamental frequency.

In stringed instruments such as the violin and guitar, or in some Indian drums such as tabla, the overtones are often close to—or exactly—whole number multiples of the fundamental frequency. However, when a string is struck or plucked, as with a piano string struck by its hammer, the string will exhibit inharmonicity. The inharmonicity of a string depends on its physical characteristics, such as tension, stiffness, and length.

Pianos

Main article: Piano acoustics – Inharmonicity and piano size

In 1943, scientists discovered that piano tones have a special quality called inharmonicity. This means that higher tones in a piano sound a bit sharper than we might expect. Interestingly, this inharmonicity is what helps piano tones sound warm and natural. Electronic instruments try to copy this quality to sound more like real pianos.

Piano tuners must account for inharmonicity, especially in the lower and higher notes. Because of this, octaves—the notes that sound the same but at double the pitch—are tuned slightly wider than usual. Tuning machines try to copy what a tuner does by ear, but tuning by ear remains an art that considers how pleasant the notes sound together. Rust or dirt on piano strings can also affect how inharmonicity sounds.

Guitar

Guitars, such as acoustic and electric guitars, are usually tuned by the players themselves. When tuning by ear, guitarists need to consider string inharmonicity, which can make notes sound sharper than they should. Even with no errors in the guitar's structure, inharmonicity can affect tuning, meaning some octaves might need small adjustments.

Electronic tuners became common in the 1970s and 1980s, but they don’t always solve tuning issues. A guitar might seem perfectly in tune on an electronic tuner, but some chords can still sound out of tune because of inharmonicity from worn strings, misplaced frets, or other problems. Cleaning the strings can help improve tuning. Some performers tune their guitars to suit the main key of a piece, but they might need to make broader adjustments to keep all chords sounding good.

Mode-locking

Other stringed instruments like the violin, viola, cello, and double bass show inharmonicity when notes are plucked using the pizzicato technique. However, this inharmonicity goes away when the strings are played with a bow. The bow’s stick-slip motion is regular and keeps all the string’s resonances at exact harmonic ratios, even if it means they vibrate slightly above or below their natural frequency. This process, called mode locking, also happens in the human voice and in reed instruments such as the clarinet.

List of instruments

Some instruments create perfectly harmonic sounds. These include bowed string instruments like the violin and cello, as well as brass instruments such as the trumpet and horn. Other perfectly harmonic instruments are reed aerophones like the oboe and clarinet.

Other instruments, such as plucked string instruments including the guitar and harp, are nearly harmonic. Tuned percussion is approximately harmonic, while untuned percussion does not produce harmonic sounds.